Competitive equilibrium: There is an extensive literature on competitive prices. The main questions are existence of competitive prices, their structure, mechanisms that can find/form those prices, and their properties (including fairness, stability, and efficiency). [1]} studied two-sided matching games in which agents can have monetary transfer and show the existence of competitive prices. They also show that these prices realize core stable outcomes, and are social-welfare maximizing. The extension to the case of non-quasilinear utility is studied in [2]} and [3]}. [4]} provide an extension to multi-partner two-sided matching markets case where each worker (firm) can have multiple but a limited number of jobs (hiring positions). Further study of many-to-one matching and many-to-many matching in two-sided matching markets is provided in [5]} and [6]}. Our data sharing market is not two-sided and allows multiple partners without limitation on their number. we also consider quasilinear utilities. However, we only allow one unit of an indivisible good to be traded in each directed partnership. Considering an additive structure on the utility function, we establish the existence of competitive prices for this setup, and we show that every social-welfare-maximizing outcome can be implemented with competitive prices such that it will be a stable outcome.
